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# Professional Development Session for Teachers in California by singaporemath.com April 2010

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William Jackson presented the morning session. Yeap Ban Har presented this in the afternoon.

William Jackson presented the morning session. Yeap Ban Har presented this in the afternoon.

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• 1. Theoretical Underpinnings of Singapore Math
Sheraton San Diego Mission Valley Hotel, San Diego CA
SingaporeMath.com
Professional Development
Yeap Ban-Har, Ph.D.
National Institute of Education
Nanyang Technological University
Singapore
banhar.yeap@nie.edu.sg
DaQiao Primary School
• 2. Catholic High School (Primary)
• 3. video of dice problem
solving problems
instructional models
overview
Bruner’s theory
Skemp’s theory
Dienes’ theory
• 4. introduction
Wellington Primary School
Lesson Study Problem
Wellington Primary School
Move 3 sticks to make 3 squares.
Move 3 sticks to make 3 squares.
Move 3 sticks to make 3 squares.
Move 3 sticks to make 2 squares.
Move 3 sticks to make 2 squares.
Move 3 sticks to make 2 squares.
• 11. A Problem from Singapore Grade 6 National Test
Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.
Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.
How many sweets did Ken buy?
• 12. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?
chocolates
sweets
Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.
12
Jim
12
18
12
12
12
12
Ken
3 parts  12 + 12 + 12 + 12 + 18 = 66
1 part  22
Half of the sweets Ken bought = 22 + 12 = 34
So Ken bought 68 sweets.`
• 13. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
A Problem from a Singapore Classroom
Fairfield Methodist Primary School
• 14.
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
• 15. 88
34
54
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
• 16. 34 – 20 = 14
54 – 34 = 20
34
54
• 17. 3 x 7 = 21
21 girls wear goggles.
A Curriculum That Helps Average Students Reach High Achievement
• 18. TIMSS 2007
Trends in International Mathematics and Science Studies
1995
2003
2007
38
41
38
High
70
74
73
Intermediate
89
92
91
Low
96
98
97
North Vista Primary School
• 19. TIMSS 2007
Trends in International Mathematics and Science Studies
Average
Indonesia
Thailand
Malaysia
Singapore
2
3
0
40
2
High
15
12
4
70
18
Intermediate
46
44
14
88
50
Low
75
66
48
97
82
Method Used in Singapore Textbooks
• 20. Beliefs
Interest
Appreciation
Confidence
Perseverance
Monitoring of one’s own thinking
Self-regulation of learning
Attitudes
Metacognition
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Mathematical Problem Solving
Reasoning, communication & connections
Thinking skills & heuristics
Application & modelling
Skills
Processes
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
Mathematics Curriculum Framework
• 21. Every Child Counts
• 22. effective
mathematics
teaching
BinaBangsa School, Indonesia
• 23. Primary Mathematics 1A
Pedagogical Principle:
Bruner
• 24. Number Bonds
PCF Kindergarten TelokBlangah
• 25. Number Bonds
PCF Kindergarten TelokBlangah
• 26. Bruner
The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
Division
National Institute of Education
• 27. Division
Princess Elizabeth Primary School
• 28. Catholic High School (Primary)
• 29. mathz4kidz Learning Centre, Penang, Malaysia
bruner’s theory
concrete
A lesson from Earlybird Kindergarten Mathematics
• 30. mathz4kidz Learning Centre, Penang, Malaysia
concrete
experiences
• 31. from
concrete
to
pictorial
mathz4kidz Learning Centre, Penang, Malaysia
• 32. from
pictorial
to
abstract
All Kids Are Intelligent Series
• 33. mathz4kidz Learning Centre, Penang, Malaysia
symbols
• 34. using
concrete
materials
Professional Development in AteneoGrade School, Manila, The Philippines
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
• 35. Primary Mathematics (Standards Edition) 2A
Pictorial Before Abstract
• 36. bruner
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
• 37. skemp’s
theory
conceptual
understanding
BinaBangsa School, Semarang, Indonesia
• 38. Keys Grade School, Manila, The Philippines
• 39. Keys Grade School, Manila, The Philippines
• 40. Skemp
Understanding in mathematics
relational
(conceptual)
instrumental
(procedural)
conventional
Teaching for conceptual understanding is given emphasis in Singapore Math.
Pedagogical Principle:
Skemp
Primary Mathematics Standards Edition Grade 6
• 41. Fraction Division
Primary Mathematics Standards Edition Grade 6
• 42. skemp
Scarsdale Middle School New York
• 43. Dienes
Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.
Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition
Primary Mathematics Standards Edition Grade 1
• 44. Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 1
• 45. Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 2
• 46. homework
Are you able to see how these tasks are varied according to Dienes’ idea of mathematical variability?
• 47. How is Task 4 different from Task 5?
16
Primary Mathematics Standards Edition Grade 5
• 48. 16
What is the given in Task 5? What is the given in Task 6? Are these different?
30
Primary Mathematics Standards Edition Grade 5
• 49. Earlybird Kindergarten Mathematics
Standards Edition
Can you see how Dienes’ idea is used in designing these tasks?
diene’s
theory
of
variation
• 50. dienes
Princess Elizabeth Primary School, Singapore
• 51. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding
• 52. conclusion
PCF Kindergarten PasirRis
• 53. Instructional Models
DaQiao Primary School
• 57. “Children are trulythe future of our nation. “
Irving Harris
• 58. This presentation is based on part of one of Singapore pre-service mathematics method courses.
50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists.
The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.
• 59. TEDS-M Elementary Teachers
Content Knowledge
TEDS-M Elementary Teachers
Pedagogical Content Knowledge
• 60. TEDS-M Middle School Teachers
Content Knowledge
TEDS-M Middle School Teachers
Pedagogical Content Knowledge